We report on the mean-field study of the Chiral Magnetic Effect (CME) in static magnetic fields within a simple model of a parity-breaking Weyl semimetal given by the lattice Wilson-Dirac Hamiltonian with constant chiral chemical potential. We consider both the mean-field renormalization of the model parameters and nontrivial corrections to the CME originating from re-summed ladder diagrams with arbitrary number of loops. We find that on-site repulsive interactions affect the chiral magnetic conductivity almost exclusively through the enhancement of the renormalized chiral chemical potential. Our results suggest that nontrivial corrections to the chiral magnetic conductivity due to inter-fermion interactions are not relevant in practice, since they only become important when the CME response is strongly suppressed by the large gap in the energy spectrum.

We study the static electric current due to the Chiral Magnetic Effect in samples of Weyl semimetals with slab geometry, where the magnetic field is parallel to the boundaries of the slab. We use the Wilson-Dirac Hamiltonian as a simplest model of parity-breaking Weyl semimetal with two-band structure. We find that the CME current is strongly localized at the open boundaries of the slab, where the current density in the direction of the magnetic field approaches the conventional value j = µ 5 B 2π 2 at sufficiently small values of the chiral chemical potential µ 5 and magnetic field B. On the other hand, very large values of magnetic field tend to suppress the CME response. We observe that the localization width of the current is independent of the slab width and is given by the magnetic length l B = 1/ √ B when µ 5 √ B. In the opposite regime when µ 5 √ B the localization width is determined solely by µ 5 .

We demonstrate the nonrenormalization of the chiral separation effect (CSE) in quenched finite-density QCD in both confinement and deconfinement phases using a recently developed numerical method which allows us, for the first time, to address the transport properties of exactly chiral, dense lattice fermions. This finding suggests that CSE can be used to fix renormalization constants for axial current density. Explaining the suppression of the CSE which we observe for topologically nontrivial gauge field configurations on small lattices, we also argue that CSE vanishes for self-dual non-Abelian fields inside instanton cores.

We perform a mean-field study of the phase diagram of interacting Weyl semimetals with broken parity, that is, with different densities of right-and left-handed quasiparticles. As a simple model system, we consider the Wilson-Dirac Hamiltonian with the chiral chemical potential and on-site repulsive interactions. We find that the chiral chemical potential somewhat shrinks the region of the pion condensation (Aoki phase) in the parameter space of the bare mass and the interaction strength, so that the condensation thresholds are at smaller interaction strengths. The renormalized chiral chemical potential monotonously grows with interaction strength everywhere in the phase diagram, and only the growth rate is discontinuous across the phase transition lines. These findings are in full agreement with previous results obtained by one of the authors for the continuum Dirac Hamiltonian, except for the fact that for our lattice model with explicitly broken chiral symmetry the boundaries of the Aoki phase remain sharp second-order phase transitions even at nonzero chiral chemical potential and there are no signatures of Cooper-type instabilities in the weakly interacting regime.

Perturbative expansions in many physical systems yield 'only' asymptotic series which are not even Borel resummable. Interestingly, the corresponding ambiguities point to nonperturbative physics. We numerically verify this renormalon mechanism for the first time in two-dimensional sigma models, that, like four-dimensional gauge theories, are asymptotically free and generate a strong scale through dimensional transmutation. We perturbatively expand the energy through a numerical version of stochastic quantization. In contrast to the first energy coefficients, the high order coefficients are independent on the rank of the model. Technically, they require a sophisticated analysis of finite volume effects and the continuum limit of the discretized model. Although the individual coefficients do not grow factorially (yet), but rather decrease strongly, the ratio of consecutive coefficients clearly obey the renormalon asymptotics.